Stocking Under Random Demand and Product Variety: Exact Models and Heuristics

Abstract

Efficient inventory management in the face of product variety is an important part of retail operations management. In this paper, we analyze the optimal stocking policy for a retailer, in a setup with a single horizontally differentiated product with an arbitrary number of product variants, stochastic demand, and two-level consumer choice. The demands for individual product variants are negatively correlated conditional on the total demand. We assume that each customer will purchase one unit of a preferred product variant, if it is in stock, and will seek to buy a second choice product, if the former is not in stock. We formulate an exact model, with Poisson customer arrivals. In order to maintain tractability and characterize an optimal policy analytically, we develop a benchmark model which does not explicitly account for the stochastic nature of customer arrival times. In this model, which is a heuristic approximation of the exact model we find simple conditions under which the objective of maximizing expected profit is jointly concave in the stocking levels of the product variants; under these conditions we prove that the optimal stocking levels are simply scaled versions of the optimal newsvendor quantities. We then analytically establish a connection between the exact and benchmark models. We develop a dynamic Monte Carlo simulation to gain further insights on the impact of different performance measures on the effectiveness of the optimal policy in the benchmark model and its performance in reference to the exact optimal policy.

Keywords: Inventory Management, Product Substitution, Horizontal Differentiation, Newsvendor Model, Product Variety